Space of modular forms of level 252 and weight 5

• Label: 252.5
• Level: 252
• Weight: 5
• Dimension: 3012
• Nonzero newspaces: 20
• Sturm bound: 17280
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(17280\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(252))\).

	Total	New	Old
Modular forms	7152	3100	4052
Cusp forms	6672	3012	3660
Eisenstein series	480	88	392

Trace form

3012 * q - 3 * q^2 + 18 * q^3 + 17 * q^4 - 3 * q^5 - 42 * q^6 - 97 * q^7 - 525 * q^8 + 54 * q^9 - 2 * q^10 + 207 * q^11 + 444 * q^12 - 818 * q^13 + 15 * q^14 - 150 * q^15 + 413 * q^16 + 1131 * q^17 - 156 * q^18 - 3 * q^19 - 1770 * q^20 + 267 * q^21 - 2730 * q^22 + 1161 * q^23 + 1890 * q^24 + 6310 * q^25 + 2466 * q^26 - 1926 * q^27 + 4353 * q^28 - 3234 * q^29 + 7698 * q^30 - 621 * q^31 + 2427 * q^32 - 12912 * q^33 - 11882 * q^34 - 10683 * q^35 - 12114 * q^36 - 475 * q^37 - 15984 * q^38 + 11202 * q^39 - 602 * q^40 + 16392 * q^41 + 2136 * q^42 - 2600 * q^43 + 6990 * q^44 - 5394 * q^45 + 13038 * q^46 - 12069 * q^47 + 15402 * q^48 + 26727 * q^49 - 3897 * q^50 - 12654 * q^51 - 25622 * q^52 + 10011 * q^53 - 13932 * q^54 + 8316 * q^55 - 18945 * q^56 + 18810 * q^57 + 27388 * q^58 + 27351 * q^59 + 30750 * q^60 + 15775 * q^61 + 50532 * q^62 + 4941 * q^63 + 18533 * q^64 - 34404 * q^65 + 26442 * q^66 - 28771 * q^67 - 17958 * q^68 + 16590 * q^69 - 42342 * q^70 + 10296 * q^71 + 8520 * q^72 - 6989 * q^73 + 906 * q^74 + 21006 * q^75 + 4098 * q^76 - 64554 * q^77 - 14136 * q^78 + 7355 * q^79 - 810 * q^80 - 78810 * q^81 + 18910 * q^82 - 74034 * q^83 - 69126 * q^84 - 60166 * q^85 - 127068 * q^86 - 57348 * q^87 - 83052 * q^88 + 50703 * q^89 - 95166 * q^90 + 39138 * q^91 + 27264 * q^92 + 140724 * q^93 + 25728 * q^94 + 183753 * q^95 + 127200 * q^96 + 63148 * q^97 + 104979 * q^98 + 39318 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(252))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
252.5.c	\(\chi_{252}(197, \cdot)\)	252.5.c.a	8	1
252.5.d	\(\chi_{252}(181, \cdot)\)	252.5.d.a	2	1
		252.5.d.b	2
		252.5.d.c	4
		252.5.d.d	6
252.5.g	\(\chi_{252}(127, \cdot)\)	252.5.g.a	12	1
		252.5.g.b	12
		252.5.g.c	12
		252.5.g.d	24
252.5.h	\(\chi_{252}(251, \cdot)\)	252.5.h.a	8	1
		252.5.h.b	56
252.5.m	\(\chi_{252}(65, \cdot)\)	252.5.m.a	64	2
252.5.p	\(\chi_{252}(61, \cdot)\)	252.5.p.a	64	2
252.5.q	\(\chi_{252}(143, \cdot)\)	n/a	128	2
252.5.r	\(\chi_{252}(131, \cdot)\)	n/a	376	2
252.5.s	\(\chi_{252}(83, \cdot)\)	n/a	376	2
252.5.u	\(\chi_{252}(151, \cdot)\)	n/a	376	2
252.5.v	\(\chi_{252}(43, \cdot)\)	n/a	288	2
252.5.y	\(\chi_{252}(163, \cdot)\)	n/a	156	2
252.5.z	\(\chi_{252}(73, \cdot)\)	252.5.z.a	2	2
		252.5.z.b	4
		252.5.z.c	4
		252.5.z.d	4
		252.5.z.e	6
		252.5.z.f	6
252.5.bc	\(\chi_{252}(13, \cdot)\)	252.5.bc.a	64	2
252.5.bd	\(\chi_{252}(229, \cdot)\)	252.5.bd.a	64	2
252.5.bg	\(\chi_{252}(29, \cdot)\)	252.5.bg.a	48	2
252.5.bh	\(\chi_{252}(137, \cdot)\)	252.5.bh.a	64	2
252.5.bk	\(\chi_{252}(53, \cdot)\)	252.5.bk.a	20	2
252.5.bl	\(\chi_{252}(67, \cdot)\)	n/a	376	2
252.5.bn	\(\chi_{252}(47, \cdot)\)	n/a	376	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)